Effective supply chain planning for a product requires not only forecasting future demands but also modeling the uncertainty in future demand. Capacity planning methods such as stochastic optimization based on the sample average approximation, involve generating scenarios for future demands simultaneously for many components. This requires that demand forecasts be supplied as predictive distributions, or “range forecasts”; traditional single-valued forecasts, or “point forecasts”, are insufficient for scenario generation.
Many products can be configured with various options when purchasing. For example, customers may request or attach optional configurations on equipment that they are purchasing. Attention then focuses on forecasting the attach rates (the proportion of the product for which a particular option is requested) for each option. Various options that can be attached may be structured in a hierarchical framework. In such a hierarchical framework forecasts may be required for thousands of option attach rates simultaneously. Estimating and using a predictive distribution in its full generality, permitting all possible dependencies between different options, is a computationally intractable problem.
Known solutions to the problem make forecasts for attach rates individually or a few at a time, and combine them into a predictive distribution by assuming independence between the separately forecast attach rates. This approach is unable to capture any but the simplest of dependences between demand for different options, and risks making systematically inaccurate judgments of future capacity requirements.